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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On generators of $ L/R\sp 2$ Lie algebras


Author: Vladimir Shpilrain
Journal: Proc. Amer. Math. Soc. 119 (1993), 1039-1043
MSC: Primary 17B01; Secondary 17B40
MathSciNet review: 1154249
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Abstract: Let $ L$ be a free Lie algebra of finite rank $ n$ and $ R$ its arbitrary ideal. A necessary and sufficient condition for $ n$ elements of the Lie algebra $ L/{R^2}$ to be a generating set is given. In particular, we have a criterion for $ n$ elements of a free Lie algebra of rank $ n$ to be a generating set which is similar to the corresponding group-theoretic result due to Birman (An inverse function theorem for free groups, Proc. Amer. Math. Soc. 41 (1973), 634-638).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1154249-X
PII: S 0002-9939(1993)1154249-X
Article copyright: © Copyright 1993 American Mathematical Society